2.优秀论文一具体要求：1月28日上午汇报
1）论文主要内容、具体模型和求解算法（针对摘要和全文进行概括）；
In the part1, we will design a schedule with fixed trip dates and types and also routes. In the part2, we design a schedule with fixed trip dates and types but unrestrained routes.
In the part3, we design a schedule with fixed trip dates but unrestrained types and routes.
In part 1, passengers have to travel along the rigid route set by river agency, so the problem should be to come up with the schedule to arrange for the maximum number of trips without occurrence of two different trips occupying the same campsite on the same day.
In part 2, passengers have the freedom to choose which campsites to stop at, therefore the mathematical description of their actions inevitably involve randomness and probability, and we actually use a probability model. The next campsite passengers choose at a current given campsite is subject to a certain distribution, and we describe events of two trips occupying the same campsite y probability. Note in probability model it is no longer appropriate to say that two trips do not meet at a campsite with certainty; instead, we regard events as impossible if their probabilities are below an adequately small number. Then we try to find the optimal schedule.
In part 3, passengers have the freedom to choose both the type and route of the trip; therefore a probability model is also necessary. We continue to adopt the probability description as in part 2 and then try to find the optimal schedule.
In part 1, we find the schedule of trips with fixed dates, types (propulsion and duration) and routes (which campsites the trip stops at), and to achieve this we use a rather novel method. The key idea is to divide campsites into different “orbits”that only allows some certain trip types to travel in, therefore the problem turns into several separate small problem to allocate fewer trip types, and the discussion of orbits allowing one, two,
three trip types lead to general result which can deal with any value of Y. Particularly, we let Y=150, a rather realistic number of campsites, to demonstrate a concrete schedule and the carrying capacity of the river is 2340 trips.
In part 2, we find the schedule of trips with fixed dates, types but unrestrained routes. To better describe the behavior of tourists, we need to use a stochastic model（随机模型）. We assume a classical probability model and also use the upper limit value of small probability to define an event as not happening. Then we use Greedy algorithm to choose the trips added and recursive algorithm together with Jordan Formula to
calculate the probability of two trips simultaneously occupying the same campsites. The carrying capacity of the river by this method is 500 trips. This method can easily find the
optimal schedule with X given trips, no matter these X trips are with fixed routes or not. In part 3, we find the optimal schedule of trips with fixed dates and unrestrained types and routes. This is based on the probability model developed in part 2 and we assign the choice of trip types of the tourists with a uniform distribution to describe their freedom to choose and obtain the results similar to part 2. The carrying capacity of the river by this method is 493 trips. Also this method can easily find the optimal schedule with X given trips, no matter these X trips are with fixed routes or not.
2）论文结构概述（列出提纲，分析优缺点，自己安排的结构）；
1 Introduction 2 Definitions
3 Specific formulation of problem 4 Assumptions
5 Part 1 Best schedule of trips with fixed dates, types and also routes.
5.1 Method
5.1.1 Motivation and justification 5.1.2 Key ideas
5.2 Development of the model
5.2.1Every campsite set for every single trip type 5.2.2 Every campsite set for every multiple trip types 5.2.3One campsite set for all trip types
6 Part 2 Best schedule of trips with fixed dates and types, but unrestrained routes.
6.1 Method
6.1.1 Motivation and justification 6.1.2 Key ideas
6.2 Development of the model 6.2.1 Calculation of p(T,x,t)
6.2.2 Best schedule using Greedy algorithm
6.2.3 Application to situation where X trips are given
7 Part 3 Best schedule of trips with fixed dates, but unrestrained types and routes.
7.1 Method
7.1.1 Motivation and justification 7.1.2 Key ideas
7.2 Development of the model
8 Testing of the model----Sensitivity analysis
8.1Stability with varying trip types chosen in 6 8.2The sensitivity analysis of the assumption 4④ 8.3 The sensitivity analysis of the assumption 4⑥
9 Evaluation of the model
9.1 Strengths and weaknesses 9.1.1 Strengths 9.1.2 Weakness
9.2 Further discussion
10 Conclusions 11 References
12 Letter to the river managers
3）论文中出现的好词好句（做好记录）；
用于问题的转化
We regard the carrying capacity of the river as the maximum total number of trips available each year, hence turning the task of the river managers into looking for the best schedule itself.
表明我们在文中所做的工作
We have examined many policies for different river….. 问题的分解
We mainly divide the problem into three parts and come up with three different…. 对我们工作的要求：
Given the above considerations, we want to find the optimal。。 阐述对问题研究后的发现和成果
We have undertaken an extensive examination of the problem and here are our key findings, hope they are beneficial to your management of the river. 自我评价（夸奖）自己的模型（模型的方法新颖） we develop a rather novel method here.
The advantages of this model are that it provides with a simple but almost optimal
schedule and that it is able to control the proportions of the number of all trip types, which makes sense to you for easier management of the river trips.
。。。做，。。。达到了。。。的简化，使得更易求解。。。
美国数学建模竞赛优秀论文阅读报告
